by
DOCTOR OF PHILOSOPHY
WOODS HOLE OCEANOGRAPHIC INSTITUTION
March 1984
Signature of Author. Department of Earth and Planetary $ciences, Massachusetts Institute of Technology and the Joint Program in Oceanography, Massachusetts Ins titute echnology/Woods Hole Qc~nographic Institution, March, 1984.
Certified by.........
Thesis Supervisor
JUN 11 1
by
Submitted to the Massachusetts Institute of Technology - Woods Hole Oceanographic Institution
Joint Program In Oceanography on March, 1984 in partial fulfillment of the
requirements for the Degree of Doctor of Philosophy
ABSTRACT
The offshore tide becomes distorted as it propagates into shallow inlet/ estuarine systems. Time asymmetries develop in the rise and fall of sea surface with consequent time and magnitude asymmetries in tidal currents. Flood-dominant estuaries are characterized by longer falling tides and stronger flood currents while ebb-dominant estuaries have longer rising tides and stronger ebb currents. The asymmetries are reflected in the non- linear growth of harmonics and compound tides of the principal equilibrium tidal constituents. This dissertation consists of three papers which examine the development of tidal asymmetries in shallow estuarine systems: a study of the recent migration history of Nauset Inlet (MA), a shallow estuarine system located on Cape Cod; an analysis of the results of a series of field experiments conducted at Nauset; a numerical model study of the types of estuarine characteristics controlling tidal asymmetry. The ana- lysis of field results focuses on sea surface measurements. Non-linear distortion of the tide at Nauset is characterized by the strong growth of harmonics and compound constituents particularly in the quarter-diurnal band. Phase relationships between the forced constituents and their parents produce a flood-dominant estuary. Numerical modeling of M2 tidal propaga- tion in shallow estuarine channels utilizes the one-dimensional equations of motion. Shallow, frictionally dominated channels with moderate tidal flat area develop a flood-dominant asymmetry while deeper channels with extensive tidal flats develop an ebb-dominant asymmetry. Model results are supported by observations of tidal asymmetry in natural estuaries. Implications of non-linear tidal distortion on bedload and suspended material transport are profound. Flood-dominant estuaries tend to import sediment if the supply is adequate whereas ebb-dominant estuaries can flush entering sediment effectively. Over long time periods, flood-dominant estuaries may eventually fill. Ebb-dominant estuaries may represent more stable long-term configurations.
Thesis Supervisor: Dr. David G. Aubrey
Title: Associate Scientist Woods Hole Oceanographic Institution
-3-
ACKNOWLEDGEMENTS
This study was supported by the Department of Commerce, NOAA Office of
Sea Grant under Grant numbers NA79AA-D-00102 and NA80AA-D-00077, the U.S.
Army Research Office under Grant DAAG 29-81-K-0004, the Woods Hole Oceano-
graphic Institution's Coastal Research Center and the W.H.O.I. education
program.
I would like to express my appreciation to Dave Aubrey for his support,
guidance and friendship over the past five and one half years. His enthu-
siasm and dedication to students made this an enjoyable experience despite
some occassionally difficult moments.
I thank Bill Grant for many useful discussions and also for his help
in learning fluid mechanics my first two years in the program. Keith
Stolzenbach, Dale Haidvogel and John Milliman provided valuable advice and
also read and commented on this thesis.
Steve Gegg and Wayne Spencer were primarily responsible for collection
of the field data (under conditions which were sometimes less than ideal).
Pam Barrows typed the manuscript.
I thank the members and friends of the WHMC especially Paul, Kenny,
Scott, Larry, John, Mike, Betsey and Char for their friendship. We had
some good times. I especially thank Susan for her love and support through
the past three years.
I thank the students and staff of G & G for their friendship, advice
and support.
Finally, I thank my parents. This work would have been difficult to
complete without their constant encouragement and support.
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IN SHALLOW
100 104
CHAPTER 1.
CHAPTER 2.
CHAPTER 3.
--5-
Shallow estuarine/tidal marsh systems connected to the ocean by a
narrow inlet are ubiquitous features along barrier beach coastlines.
Barrier beaches and their associated tidal inlets comprise approximately
13% of the world's coastline (King, 1972), most occurring in areas with
low to moderate tidal range. The longest stretch of barrier beaches and
tidal inlets in the world is located along the U.S. East and Gulf of Mexico
coasts, affording protection to over 5000 km of navigable waters. Inlet/
estuarine systems along these coastlines play important roles in the bio-
logical cycles of many organisms and in nutrient exchange with coastal
waters. In addition, many are used, or are intended for use, as naviga-
tional channels. As the offshore tide propagates into these systems, it
can become distorted as a result of non-linear fluid mechanical proces-
ses. The tidal distortion takes the form of time asymmetries in the rise
and fall of sea surface and consequent time/magnitude asymmetries in tidal
currents. Patterns of sediment transport and nutrient/pollutant exchange
can be strongly affected by the tidal distortion. The long term stability
and evolution of these estuaries are partly controlled by their response
to tidal forcing.
Coastal geologists have focused on the velocity asymmetries frequently
observed in the tidal inlet channel and classified inlets as either "ebb
dominant" or "flood dominant" (eg., Hayes, 1975). Many inlet channels are
termed "ebb dominant" because it is observed that ebb currents continue to
flow even after the ocean tide has turned to rise. As a result, flood cur-
rents are confined to shallow channels on either side of the main inlet
channel during early stages of rising tide (see figure 1 for inlet morpho-
logy). This situation is caused by lags in low water from the ocean to the
far reaches of the estuary. The terms "ebb dominant" and "flood dominant"
DOMINANT \WAVE DIRECTION
-- - - - - EBB TIDAL DELTA
AL AL AL AL
AL AL AL AL A~ AL AL ~ -~ AL AL AL~e. AL AL AL AL AL AL .~e AL AL
AL AL AL AL
AL AL AL AL
AL -~ AL AL
l-
Figure 1. Sketch of dominant morphologic features in a tidal inlet.
MARGINAL FLOOD CHANNEL
AL~ ~
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have generally been applied to currents at the inlet as opposed to further
within the estuary. Although most work has focused on the time-velocity
asymmetry of tidal currents investigators have noted the time asymmetry
present in sea surface (eg., Byrne et al., 1975; Boon and Byrne, 1981;
FitzGerald and Nummedal, 1983). The duration asymmetry in rising and
falling tide can impart an ebb or flood dominance to the estuary as a
whole. For example, an estuary characterized by a longer rising tide will
tend to have stronger ebb currents ("ebb dominant"). Estuaries of both
types occur along the U.S. East coast (Table 1).
The importance of tidal asymmetries to processes such as sediment
transport (eg., Postma, 1967; Pingree and Griffiths, 1979) has long been
recognized. The presence of a distorted tidal velocity signal can produce
a net suspended and bed load transport. Within estuaries, net patterns of
sediment transport can have important implications for inlet/estuarine
stability. An estuary characterized by a longer falling tide and hence
stronger flood currents may show a pattern of net up-estuary sediment
transport. Such an estuary may be unable to flush effectively sediments
entering the system through the inlet. As a result, the estuary could be
expected to gradually fill, with consequent reduction of tidal prism and
development of channel shoaling problems. The tidal response of these
systems, therefore, may play an important role in their geological develop-
ment. Some investigators, in fact, have hypothesized that an inlet/estuar-
ine system could evolve from a flood-dominant transport pattern in its
early stages to ebb-dominant as the estuary filled (Byrne and Boon, 1976).
Such a development implies a feedback between estuarine geometry and tidal
forcing.
-9-
Longer falling tide ("flood dominant")
Murrells Inlet, S.C.
Nauset Inlet, MA
Wachapreague Inlet, VA
North Inlet, S.C.
Price Inlet, S.C.
Boon and Byrne, 1981
Nummedal and Humphries, 1978
Fitzgerald and Nummedal, 1983
Over shorter time scales, many investigators have been interested in
patterns of net suspended material transport. This is particularly impor-
tant for biologists concerned whether inlet/marsh systems export dissolved
and particulate nutrients into coastal waters (Valiela et al., 1978; Teal,
1983). Nutrient circulation depends in part on transformations which occur
in the tide as it propagates into these shallow systems. Net patterns of
suspended material transport have been explained by means of the time-
velocity asymmetries developed in estuarine channels (eg. Boon, 1975;
Ward, 1981).
Despite the large number of problems studied in shallow estuaries, few
have focused on the tidal propagation problem itself. However, it is the
interaction of estuarine geometry and tidal forcing which produces the
observed asymmetries in tidal currents and the rise and fall of sea
surface. A number of investigators have utilized numerical models to
investigate the role of estuarine hypsometry in distorting the tide (Mota-
Oliveira, 1970; Seelig and Sorensen, 1978; Boon and Byrne, 1981). These
studies have not been sufficiently systematic. In addition, they did not
focus on the spectral response of the model estuaries to tidal forcing.
This is important because the non-linear process of tidal distortion
observed in the field reveals itself in the growth of harmonics of the
principal astronomic constituents.
Data sets obtained in the field have largely consisted of 12 or 24 hour
cycles of velocity measurements typically sampled at hourly intervals.
These measurements frequently have been concentrated near the inlet channel
(eg., Boothroyd and Hubbard, 1975; Finley, 1975; Hine, 1975; Nummedal and
Humphries, 1978; FitzGerald and Nummedal, 1983). Long-term records of sea
surface measurements (sufficient for harmonic analysis) are sparse, with
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only a few comprehensive surveys (e.g.-, NOS experiment, Murrells Inlet,
SC, Boon and Byrne, 1981). A comprehensive field program supported by
modeling is required to understand tidal propagation in these shallow
systems. The key questions are: What are the kinematics and mechanics of
the non-linear distortion of the tide within a shallow estuary? What are
the geometry and friction characteristics of estuaries which produce the
different types of asymmetry? The present study addresses these questions.
It has involved a field study at Nauset Inlet, MA, a tidal inlet/marsh
complex representative of many such features along the U.S. east coast.
In addition, numerical modeling was employed as a diagnostic tool to
investigate the important aspects of tidal propagation identified by the
field experiments.
The thesis consists of three papers (co-authored with D. Aubrey): a
study of the recent migration history of Nauset Inlet; an analysis of the
results of a series of field experiments conducted at Nauset; a numerical
model study of the types of estuarine characteristics responsible for
producing different tidal asymmetries. The first paper places the field
experiments within the framework of the recent history of the inlet/
estuarine system. The Nauset estuary/marsh complex is serviced by an
unstable inlet which has migrated as much as 2 km over the past 30 years.
The inlet is presently moving north at approximately 100 m/yr and is more
than 2 km from an historically preferred location. Such large-scale migra-
tion changes the lengths of estuarine tidal channels and can affect its
tidal response. This paper examines the migration episodes and formulates
three hypotheses explaining the observed behavior.
The second paper discusses results from field experiments designed to
examine tidal propagation in this shallow estuary. The analysis focuses
on sea surface elevation measurements, supplementing them with velocity
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records which illustrate the type of tidal asymmetry developed at Nauset.
The non-linear distortion of the tide is characterized by the growth of
harmonics and compound constituents of the primary astronomic frequencies.
Sea surface records of sufficient length to examine this problem spectrally
are far easier to obtain than velocity records. In fact, difficult environ-
mental conditions (shallow water, strong flows, extreme sediment transport
rates) preclude long velocity records from most regions of the estuary.
Hence velocity is used as supplementary information to a detailed investi-
gation of sea surface records.
The numerical section presents results from one-dimensional (cross-
sectionally averaged) modeling of estuarine characteristics contributing
to different forms of tidal asymmetry. The modeling is diagnostic and
does not attempt to predict or hindcast conditions at Nauset. These
systems are physically complex and require two-dimensional models to
hindcast sea surface and depth-mean velocity. Such models exist (eg.,
Masch et al., 1977; Butler, 1980) but they do not explain what drives
estuaries to different tidal responses. In addition, their ability to
represent non-linear estuarine dynamics accurately is unclear since
investigators have not provided spectral comparisons of field data with
model solutions. The one-dimensional models are used to examine the role
of channel cross-section shape, tidal flats and variable levels of friction
in distorting the estuarine tide. Model results indicate systems with
strongly time-variable channel cross-section and moderate extent of tidal
flats tend to be flood-dominant. Conversely, estuaries with extensive
tidal flats and less time-variability in channel geometry are ebb-dominant.
Results of the field experiments at Nauset Inlet and observations of tidal
asymmetry in other shallow estuaries support the findings of the model study.
-13-
REFERENCES
Boon, J.D., 1975. Tidal discharge asymmetry in a salt marsh drainage
system. Limnol. Oceanog., v. 3, p. 71-80.
Boon, J.D. and R.J. Byrne, 1981. On basin hypsometry and the morpho-
dynamic response of coastal inlet systems. Marine Geology, v. 40,
p. 27-48.
Boothroyd, J.C. and D.K. Hubbard, 1975. Genesis of bedforms in mesotidal
estuaries. In L. Eugene Cronin (ed.), Estuarine Research, v. 2,
Academic Press, p. 217-234.
Butler, H.L., 1980. Evolution of a numerical model for simulating long-
period wave behavior in ocean-estuarine systems. Estuarine and
Wetland Processes with Emphasis on Modeling, Marine Science Series,
v. 11, Plenum Press, p. 147-182.
Byrne, R.J., P. Bullock and D.G. Tyler, 1975. Response characteristics of
a tidal inlet: A case study. In L. Eugene Cronin (ed.), Estuarine
Research, v. 2, p. 201-216.
Byrne, R.J. and J.D. Boon, III, 1976. Speculative hypothesis on the evolu-
tion of barrier island - inlet - lagoon systems. Geol. Soc. Am.,
NE/SE Sect. Ann. Meet., Abstr., v. 8, p. 159.
Finley, R.J., 1975. Hydrodynamics and tidal deltas of North Inlet, South
Carolina. In L. Eugene Cronin (ed.), Estuarine Research, v. 2, p.
277-292.
FitzGerald, D.M. and D. Nummedal, 1983. Response characteristics of an
ebb-dominated tidal inlet channel. Jour. Sed. Pet., v. 53, p. 833-845.
-14-
Hayes, M.O., 1975. Morphology of sand accumulation in estuaries: An
introduction to the symposium. In L. Eugene Cronin (ed.), Estuarine
Research, v. 2, p. 3-22.
Hine, A.C., 1975. Bedform distribution and migration patterns on tidal
deltas in the Chatham harbor estuary, Cape Cod, Mass. In L. Eugene
Cronin (ed.), Estuarine Research, v. 2, p. 235-252.
King, C.A.M., 1972. Beaches and Coasts, Edward Arnold Ltd., London,
570 pp.
Masch, F.D., R.J. Brandes and J.D. Reagan, 1977. Comparison of numerical
and physical hydraulic models, Masonboro Inlet, North Carolina.
Appendix 2, v. 1, Numerical simulation of hydrodynamics (WRE). GITI
Report 6, U.S. Army Coastal Eng. Res. Cent., 123 pp.
Mota-Oliveira, I.B., 1970. Natural flushing ability in tidal inlets. In
Am. Soc. Civ. Eng., Proc. 12th Coastal Eng. Conf., p. 1827-1845.
Nummedal, D. and S.M. Humphries, 1978. Hydraulics and dynamics of North
Inlet, South Carolina, 1975-1976. GITI Report 16, U.S. Army Coastal
Eng. Res. Cent., 214 pp.
Pingree, R.D. and D.K. Griffiths, 1979. Sand transport paths around the
British Isles resulting from M2 and M4 tidal interactions. J.
Mar. Biol. Assoc. v. 59, p. 467-513.
Postma, H., 1967. Sediment transport and sedimentation in the estuarine
enviroment. In G.H. Lauff (ed.), Estuaries, Am. Assoc. Adv. Sci.,
p. 158-179.
Seelig, W.N. and R.M. Sorensen, 1978. Numerical model investigation of
selected tidal inlet-bay system characteristics. In Am. Soc. Civ.
Eng., Proc. 16 1 Coastal Eng. Conf., p. 1302-1319.
-15-
Teal, J.M. (ed.), 1983. The coastal impact of groundwater discharge: an
assessment of anthropogenic nitrogen loading in Town Cove, Orleans,
Massachusetts. Report to Board of Selectmen, Orleans, Mass. Woods
Hole Oceanographic Institution.
Valiela, I., J.M. Teal, S. Volkmann, D. Shafer and E.J. Carpenter, 1978.
Nutrient and particulate fluxes in a salt marsh ecosystem: tidal
exchanges and inputs by precipitation and groundwater. Limnol.
Oceanogr., v. 23, p. 798-812.
Ward, L.G., 1981. Suspended-material transport in marsh tidal channels,
Kiawah Island, South Carolina. Mar. Geology, v. 40, p. 139-154.
-16-
-17-
ABSTRACT
Three mechanisms are responsible for tidal inlet migration in an
updrift direction (counter to net longshore transport): 1) attachment of
distal ebb tide delta bars to the downdrift barrier spit; 2) storm-induced
breaching and subsequent stabilization to form a new inlet; and 3) ebb tide
discharge around a channel bend creating a three-dimensional flow pattern
which erodes the outer channel bank and accretes on the inner channel bank.
The last two mechanisms can result in either updrift or downdrift inlet
migration, depending on channel geometry in the bay and barrier beach con-
figuration. The last mechanism is discussed here for the first time.
Analysis of historical charts and aerial photographs, combined with an
historical storm synthesis, shows that all three mechanisms are active at
a natural tidal inlet along a sandy coast (Nauset Inlet, Cape Cod, MA).
On a time scale of ten years, these mechanisms were effective in producing
an updrift migration of more than two kilometers. Initiation of updrift
migration coincided with a marked increase in storm frequency perturbing
the historically stable inlet position. Subsequent updrift migration
resulted from ebb-delta bypassing and channel bend flows.
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INTRODUCTION
Migration of tidal inlets and the associated changes in adjacent
barrier beaches have profound implications on both the geological evolution
of inlet/estuary systems and the short-term stability of these features.
Past studies have documented many instances of inlets migrating in the
direction of net littoral drift along sandy shores, but have uncovered few
cases (e.g., Indian River Inlet, Delaware, and Thorsminde Inlet, Denmark)
where inlets appear to migrate in directions opposed to the dominant long-
shore transport direction (Bruun, 1978). Migration of tidal inlets in any
direction accelerates inlet-induced changes in the estuary. The estuary
may fill in with littoral sands derived from updrift sources, as flood tide
delta growth accompanies the migration of the inlet, and marsh development
(colonization and plant emergence) becomes more variable and less permanent.
Previous attempts to explain a reversal in direction of inlet migration
suggest a change in direction of net littoral drift, causing a change in
migration direction. This explanation is not realistic for some inlets
where wave forcing and nearshore bathymetry have remained constant through
time. This study presents three alternatives to explain the tendency of
some inlets to migrate updrift, each supported by historical observations
at a site with a large-volume, directionally-biased littoral drift.
The study site is located on the Atlantic coast of Cape Cod, Massa-
chusetts (figure 1), exposed to open ocean waves from the east and a two-
meter ocean tide. Offshore bathymetry and sediments are described else-
where (Aubrey, Twichell and Pfirman, 1982). Longshore transport rates and
directions were studied by Zeigler (1954, 1960), and net littoral drift
has been estimated at 250,000 m3 per year towards the south (U.S. Army
Corps of Engineers, 1969). Sediment is derived from erosion of sea cliffs
NANTUCKET SOUND
NANTUCKET SHOALS
E A
410 50'
T H
STATUTE MILE
410 50'
bordering Nauset Inlet to the north. Overwash processes along Nauset
barrier beaches are described in Zaremba and Leatherman (1979). Aubrey and
Speer (1983, 1984) discuss tidal flows and sediment transport in the bay
and inlet. Other sedimentologic studies of the region are found in a
summary volume by Leatherman (1979).
Sea level here has risen an average of about 3.5 mm/year. This rate
is three times greater than the mean sea level rise of one mm/year over
the past 2100 years established from measurements of salt marsh peat
accumulation at Barnstable Harbor, Cape Cod (Redfield and Rubin, 1962).
As discussed by Aubrey and Emery (1983) and others, although short-term
mean sea level records exhibit considerable oscillations about a mean
trend, the mean rate over the past 100 years has not changed significantly.
Sea-level rise favors landward migration of evolving barrier beaches.
METHODS
Historical charts and aerial photographs of the Nauset Inlet area
dating from 1670 and 1938, respectively, were examined to define and (where
possible) quantify changes in inlet position and morphology. Historical
data (figure 2) were obtained from a variety of sources including govern-
ment agencies, the National Archives, the Library of Congress, the Woods
Hole Oceanographic Institution, and private industry (Speer, Aubrey and
Ruder, 1982; Appendices 1 and 2). Chart coverage is dense from 1790 to
present (coverage was sparse before 1790), and good aerial photographic
coverage exists from 1951 to present (only one aerial photo sequence was
available prior to 1951, taken in 1938). Small scale and uncertain mapping
techniques used in pre-1846 historical charts make it difficult to quantify
changes in inlet morphology during this period, but these charts were valu-
able in depicting general trends in inlet morphology. Care was required in
NAUSET INLET
AERIAL PHOTOGRAPHY n=125
I III III I I I I I i II I IIII 1965
NAUSET INLET HISTORICAL CHART!
1850 1900 1950 1980
Figure 2. Summary of Nauset Inlet aerial photography (125 sets since 1938) and historical charts (120 sets since 1670).
10 F
4-
S3
21
LI-
II 1750
-22-
interpreting the charts because several of the charts from the 1800's did
not specify survey dates, and were merely reproductions of earlier and
perhaps outdated surveys. Also, in the case of U.S. Coast and Geodetic
Survey (USC&GS) charts, only limited shoreline segments were updated
between editions.
Aerial photographs provide more detailed information than the charts
because they are generally larger in scale (allowing resolution of shore-
line features such as bars and marshes). They also provide more comprehen-
sive temporal coverage for a limited period (1951 to 1981) than do the
charts, and the dates of coverage are unambiguous. Fifty vertical sets of
the 125 photographs available were measured to quantify inlet and spit
migration at Nauset. The remaining photographs were not measured because
they were taken at oblique angles, were poorly fitted mosaic series, or
lacked sufficient ground control to assure measurement accuracy. However,
they were instrumental in providing a continuous record of relative changes
in inlet and spit locations during the past 30 years.
Measurements of spit and inlet locations are relative to a baseline,
sub-parallel to the shoreline, established between well-defined, permanent
features identified on each set of aerial photographs (figure 3). The
known length of this baseline provided a consistent determination of scale
for all photos. Uncertainty in some measurements resulted when one of the
two primary reference points was absent from a particular photo mosaic.
In these cases, secondary landmarks were used along with geometrical rela-
tions to define the baseline from the one available endpoint. As a result
of such variations in the photographs, overall accuracy of measurements is
estimated to be + 15 m, despite a measurement resolution of 5 m.
-23-
REFERENCE POINT +
Figure 3. Baseline location for inlet migration measurements. The northern reference point adjacent to Coast Guard beach is Coast Guard Station. Distance between adjacent reference lines (1-10) is 535 m.
-24-
RESULTS
Analysis of historical charts and photographs reveals patterns of inlet
migration and barrier beach elongation/shortening at Nauset. Nauset Inlet
has migrated extensively over the past 30 years, related in part to an
increase in storm frequency, as discussed below.
INLET/BARRIER BEACH MIGRATION
Historical charts (dating from 1779) and aerial photography (dating
from 1938) show the preferred inlet location to have been just north of
Nauset Heights, at the southern (downdrift) extremity of the bay drainage
system (figure 4). None of the charts (up to 1946) depict a significant
south spit. Although aperiodic historical coverage might have undersampled
previous episodes of inlet migration, the persistence of a southern loca-
tion suggests this was an historically stable inlet configuration.
Aerial photographs from 1938 and a 1946 USGS chart confirm an inlet
location just north of Nauset Heights, with no south barrier apparent
(figures 5 and 6). From the 1950's into the early 1980's, the inlet has
been active with three distinct cycles of northward (updrift) movement.
The first two of these (figure 5; 1952-1957; 1965-1972) resulted in a pat-
tern of overlapping spits. In both cases, the length of the north spit
remained approximately stable while the south spit continually grew north.
The third cycle (figure 5; 1972-1984) has involved substantial erosion of
the north spit along with northward growth of the south spit.
The first cycle of northward growth was initiated by storm activity.
The north barrier was breached and a remnant of the barrier located south
of the new breach attached to the south barrier. Subsequent southward
growth of the north barrier through attachment to an island in the marsh
(Inlet Marsh), and northward growth of the south spit, resulted in the over-
-25-
CC9
SO
Figure 4. Five representative historical charts dep icting variability ofNauset Inlet from 1779--1910.
BARRIER BEACH LENGTHS NAUSET INLET, MA
YEAR
Figure 5. Location of North Spit and South Spit termini, measured along the baseline from Coast Guard Station (see figure 3 caption). Stippled patterns indicate periods when South Spit overlapped North Spit, and extended farther north. Vertical lines indicate periods for which measurements were made.
2000
2500 -
< 3000 -
78
-29-
lapping pattern of the mid-1950's (figure 6). During this period of
barrier growth, the elongated inlet channel extended to the north from its
original southern location. A series of storms in the late 1950's and
early 1960's re-established the inlet to its southernmost position immedi-
ately adjacent to Nauset Heights (figure 6f, 7a). By April 1965, the inlet/
barrier beach configuration was similar to that in 1938, with the sole major
difference being landward migration of the north spit due to repeated storm
overwashes (Zaremba and Leatherman, 1979). The second cycle of northward
migration was characterized by extension of the south barrier while the
north barrier remained in approximately the same location. Between 1965
and 1972, the south spit extended nearly 900 m to the north (figure 7b, 7c).
As in the mid-1950's, the inlet channel also extended north, accompanying
this barrier growth.
The final cycle of northward movement was initiated by a storm breach
in the north spit in the spring of 1972 (figure 7c). This resulted in the
present phase of northward migration which is qualitatively different from
the previous two episodes. In this third instance, the main inlet channel
stabilized in the location of the newly formed breach with the former inlet
closing off. Since 1972, the inlet channel and the south barrier have been
growing northward at a rate of approximately 100 m/yr. Unlike previous
cycles, the north spit is steadily eroding and the main inlet channel is
actually moving north, instead of simply extending to the north from a
southern location (figure 7d-7f). No major breaches affecting the stabil-
ity of the south spit have occurred during this latest period. A large
overwash occurred at the northernmost part of the north spit during the
6 February 1978 blizzard. Since this overwash emptied into a shallow
-30-
(<1 m deep), broad bay (Nauset Bay), the overwash did not evolve into a
permanent breach. Such an overwash occurring on the south spit would
probably result in a new inlet position.
STORM ANALYSIS
The Atlantic shore of Cape Cod is frequently buffeted by storms which
have the potential to cause dramatic changes in shoreline configuration.
A U.S. Army Corps of Engineers report (1979) cites 160 gales with wind
speeds greater than 32 mph between 1870-1975. Half of these were north-
easters. Both tropical and extra-tropical (including northeasters)
cyclones produce dramatic changes at Nauset Inlet because of the geograph-
ical orientation of the outer Cape.
Three types of storm data were collected for comparison with large-
scale morphologic changes at Nauset Inlet:
a) Hayden and Smith (1982) compiled a monthly list of cyclone occur-
rences off the east coast between 1885 and 1982, using as a data base the
"Tracks of the Centers of Cyclones at Sea Level" published by Monthly
Weather Review and in recent years by Mariners Weather Log. Cyclone
statistics (both tropical and extra-tropical) are available on 2.5* lati-
tude by 5* longitude grid cells. The four grid cells bordering the Cape
Cod region to the east and southeast (total area covered is 60*W to 70*W,
37i*N to 42i*N) are used as the region of storm influence for the
study area. For generation of year-by-year and monthly mean statistics,
storm values for the four grid cells are summed. Although this yields an
overestimate of the number of storms (the same storm may pass more than
one grid cell), it will still provide a qualitative indication of storm
duration and persistence, since on the average a storm tracking through
two grid cells generates waves in the study area for a longer period of
time than one passing a single grid cell.
ANNUAL STORM FREQUENCY OFF CAPE COD, MASSACHUSETTS 1885 - 1982
0 1 1885 1890 1900 1910 1920 1930 1940 1950 1960 1970
YEAR 1980
Figure 8. Number of cyclones affecting Cape Cod, Massachusetts (including area 60*W to 70*W, 37 * to 424*N) from 1885 to 1981. Storm count is indicative of storm duration, and not individual cyclone events. Data derived from Hayden and Smith (1982).
180
160
140
120
100
80
40
20
-32-
Cyclone statistics resulting from the averaging serve as a crude indi-
cator of wave activity. Large cyclone counts suggest high wave activity;
a small cyclone count represents low wave activity. Persistence and
frequency of storms are our criteria for wave intensity. Clearly, storm
intensity or magnitude would be a useful weighting factor for linking
waves and storms; unfortunately, this information is not available.
The period from 1885 through 1949 experienced a relatively low incid-
ence of storm activity (figure 8). Within this low background level, the
periods from 1885-1893, 1921-1924, and 1930-1941 have local maxima in
cyclone frequency. The last thirty years of the record show consistently
higher cyclone frequency, with local maxima at 1950-1954, 1961-1962, 1972
and 1974. Although the absolute number of storms may be sensitive to the
quality and quantity of weather observation stations, local trends (minima
and maxima) are valid indicators of relative storm occurrence.
b) Another source of storm incidence data was the U.S. Army Waterways
Experiment Station (WES) wave hindcast program (data provided by W. Birke-
meier). This program computes nearshore wave height statistics based on
weather observations and local bathymetry. The study identified the 157
largest storm events from 1956 to 1976 (inclusive). These storms were
assigned recurrence intervals according to their rankings, allowing for
weighting of storms by severity. The WES compilation (figure 9) correlates
well with cyclone data. W.E.S. data show high storm activity in 1956,
1962, and 1972; however, it also indicates a high level of storm activity
in 1969 which does not appear in cyclone data. Differences between the
two data sets are the result both of weighting procedures and different
representations of the data base.
-33-
24
22
20
18
16
44
12
10
8
6
4
2
YEAR '72
Figure 9. Yearly storm activity from 1956-1976 off Cape Cod, determined by W.E.S. hindcast.
Massachusetts,
Cr)
156 158 '60 '62 '64 174 '76
..............e a e e e e e e a a , a a e e e e . m o a y e e a e= e e e a a a . , e a . . . . . . . . ..ae e e a e e e e a e a a e e a a..... ...... ......e a e e a = . . . . .e e e . . e e e = . e e e a e a e
.. . . . . . . . . . . . . .... ..ma a e a = m e a a a e . . e e a e e a e a . . .................. .. . .. .. . .. . .. .. . .. . . . .. . ... e e e e e a e , a = m a , e a = = e a 4 e e a e a 9 e e e e e = e a e e e e e a e .m .........o...... ...... .. .... .. ....... ..... ...... ..... ..... .... .... .. ....a e e e a . a a a e .e. . .=. . .e.a.e. . .. ... . . = a e e e a . .. . . ...... ..e a e o e e a e e e
STORM FREQUENCY AT CAPE COD, MA.
00 0 ~ffl 1820 1840 1860 1880
011 DOR RH RH 1900 1920 1940 1960 1980
YEAR Figure 10. Compilation of storm events on an annual basis from 1800 through 1980.
Sources are newspapers, historical descriptions, and published tropical storm tracks.
5 LAI
4 3J~
()
1800 i I I I'll. " . 11 N I , . . . . . . . .. ... , , ... ... . . .. . ,, .. I I-LLIII 1 10 .11 111 1 11.11 1 'It '11 1 1 It IIIL- I I I I
-35-
c) Finally, a list of major storms affecting the outer Cape was com-
piled from newspapers, historical descriptions, and published tropical
storm tracks (figure 10). This list is incomplete since prior to 1948 it
only includes hurricanes and storms of historical significance. It is
possible to identify specific storms which are likely to cause changes at
Nauset Inlet, although irregular sampling afforded by aerial photography
(figure 2) makes direct correlation difficult. Through this method, ten
significant storms were found that were not hindcast in the WES study.
DISCUSSION
Aerial photographs and historical charts reveal patterns of inlet/
barrier beach change with which conceptual models must be consistent. The
important features of Nauset Inlet's migration patterns are: the histor-
ical stability of the southernmost inlet entrance; the role of storms in
initiating major changes in the inlet/barrier beach system; and the recent
tendency for the inlet to move in a direction opposite the predominant
longshore drift. Migration of the inlet with accompanying changes in the
barrier beaches takes place on essentially two different time scales.
Major relocations of the inlet, involving longshore movements of hundreds
of meters in several days, occur episodically during large storms, and have
a recurrence on the order of a decade. The other important time scale is
associated with the recent steady migration of the inlet in a general north-
ward direction, responding to the combined effects of wave activity, tidal
flows, and longshore sand transport. The magnitude of this movement is on
the order of 100 m/yr. Northward migration of the inlet is accompanied by
extension of the southern barrier and generally by shortening of the north-
ern barrier (especially from 1973-1983).
-36-
The general stability of a southern inlet location in this system is
not surprising. Most of the tidal prism passes through the deeper southern-
most channels of the marsh, therefore a southern inlet provides the most
direct link to the ocean. Frictional dominance in this shallow inlet/
estuary system (Aubrey and Speer, in prep.; Speer and Aubrey, in prep.)
makes this an energetically favorable location for the inlet. The 1983
location of the inlet requires that long (~2 km) shallow channels carry
most of the tidal prism to the south. A large fraction of the total tidal
energy is dissipated in these channels; consequently development of an
energetically more favorable inlet location further south is probable in
the near future (order of a decade).
The southernmost location places constraints on barrier beach configur-
ation. In general, the northern barrier is not strongly eroded by the ebb
tidal flows when the inlet is in a southerly location as compared to a more
northerly one (reasons for this are presented later). A short, slowly-
growing southern spit can develop without catastrophic storm influence.
However, large-scale growth of a southern barrier spit is dependent on
storm activity and breaching of the northern barrier.
Three mechanisms appear responsible for observed updrift tidal inlet
migration at Nauset (figure 11): a) attachment of distal ebb tide delta
bars to the downdrift barrier spit; b) storm-induced breaching and sub-
sequent stabilization to form a new inlet; and c) ebb tide discharge
around the inlet channel bend. The last two mechanisms can result in
either updrift or downdrift migration. The first two mechanisms have been
observed widely at other inlets; the third mechanism is described here for
the first time.
A
....~ RAY
A E Clow
<= LONGSHORE SAND TRANSPORT
Figure 11. Three modes of updrift inlet migration responding to different combinations of waves, tides and storms. All three modes have been observed at Nauset Inlet, Cape Cod, Massachusetts.
-38-
1955
ST 1955 Four month bar-bypassing event observed at Nauset Inlet, Massachusetts.
1955
-39-
a) Any model of Nauset Inlet's migration must include mechanisms for
longshore bypassing of sediment past the inlet, since the volume rate of
longshore sand transport is a primary factor controlling inlet stability
(e.g., Brunn and Gerritsen, 1959; Bruun, 1978). Large net longshore trans-
port rates, estimated to be about 250,000 m3/yr to the south (U.S. Army
Corps of Engineers, 1969), occur at Nauset Inlet. Consequently, shallow
overwashes are typically filled quickly, and the tidal prism seems capable
of supporting only a single stable inlet.
A common mode for sediment bypassing of tidal inlets is through forma-
tion and migration of distal ebb delta bars, which are predominantly wave-
driven. For many wave-influenced tidal inlets throughout the world, ebb
delta bar migration is the dominant bypassing mode (Bruun, 1978; Fitzgerald,
1983; Nummedal, 1983), while bypassing through the inlet proper (Galvin,
1983) appears less important. Bar bypassing results in episodic accretion
of sand on the downdrift barrier, often increasing encroachment of the down-
drift barrier into the inlet throat.
Bar bypassing has been documented several times at Nauset Inlet
(figure 12), increasing the length of the southern (downdrift) barrier.
The existence of active bar bypassing at Nauset causes south spit to grow
to the north, against the influence of predominant longshore transport,
since the migrating bars weld to the spit terminus instead of escaping the
inlet influence (figure 11). Although not shown on the figure, the
accreted sand remains on the downdrift spit, increasing its length, and
forcing the inlet to migrate northwards. Contrary to the observations of
Fitzgerald (1983), these accretionary episodes occur on time scales of
months, not years.
-40-
b) The importance of storm activity to major changes in inlet/barrier
beach configuration is illustrated by comparison of inlet migration rates
with storm frequency. Historical data (figures 8, 9 and 10) show three
periods of high storm activity since 1933, preceded by a 48 year period of
relative quiescence. The first period of intense activity lasted from 1933
until 1939. Unfortunately, inadequate chart and photo coverage prevents
full documentation of inlet response to this stormy period. The second
stormy period covered the years 1950 to 1962. Large scale inlet migration,
together with overwash and breaching of the barrier beaches, occurred dur-
ing this time. The north barrier breached in May 1953 and January 1956,
while the south barrier breached in December 1957 and early spring 1960.
Storm-induced changes in barrier beach length of as much as 780 m have been
observed. A third period of intense storm activity existed in the early
1970's. One of the peak years, 1972, coincides with a breach in the north
spit, which initiated the current phase of steady northward inlet migration.
c) Casual observation of tidal inlet and estuarine flows shows that
these channels often are not straight, but rather have pronounced curva-
ture. This curvature has dramatic effects on flow through these channels,
affecting near-bed shear stress distributions and resultant sediment trans-
port. Complexity of channel geometry ranges from long, straight channels
with occasional bends, to nearly continuous, sinuous geometry reminiscent
of river channel meanders. Channel curvature within an inlet mouth pro-
vides a mechanism for inlet migration, as discussed below. An extensive
literature discusses the effects of channel curvature on flow structure
and sediment transport, largely resulting from an interest in river channel
meanders and open channel flow. Much of the work to date has been done by
engineers interested in channel scour and deposition (e.g., Nouh and Town-
send, 1979), or by geologists studying riverine processes (e.g., Dietrich
00
0.-
DATUM: MEAN LOW WATER 0 0 0 400 200 300 meters
>BASS ARRAY A PRESSURE SENSOR A TL A N TI C x BENCHMARK
r, BEDFORM MONITOR OCE AN
SURVEYS FROM 26 JULY TO 2 AUGUST, 1980
Figure 13. Nauset Inlet in summer of 1980 shows the strong channel curvature responsible for 'river-bend' flow structure. Primary tidal channels in the estuary are to the south (left), causing this curved flow.
-42-
et al., 1982). Recently, more complete numerical models have quantified
aspects of channel bend flow which had been described qualitatively by
previous researchers (e.g., Smith and McLean, 1983).
Since the inlet mouth at Nauset has considerable curvature (figure 13),
sediment transport patterns are modified by resulting bed shear stress gra-
dients. To examine the magnitude of flow curvature at Nauset Inlet and
evaluate its effect on sediment transport, simple theory was developed and
tested by field observations (Aubrey and Speer, 1983). Since flow curva-
ture induces gradients in water level through a channel bend, and water
level is relatively easy to monitor compared to velocity or shear-stress
distribution, modeling and measurement efforts concentrated on surface gra-
dients across the inlet mouth.
For simple geometry and quasi-steady channel flows, the along-channel (n)
momentum equation reduces to a simple balance between the bottom stress
(T) and the sea surface gradient (an/an):
tb = -pgh an/an (1)
where h = mean water depth, p is density of water, and g is gravitational
acceleration. If the downstream set-down is measured, an estimate of total
bottom friction is obtained. The lowest order equation for cross-stream
flow reduces to:
U2 _ (2)
gR ar
for the case of small channel half-width (b) compared to radius of curva-
ture (R). U is the depth-averaged velocity. For a sinusoidal channel, the
cross-stream gradient reduces to:
-43-
is obtained from equation (1) and
tb = PCE U2, (4)
where Cf is a friction coefficient. Then the cross-channel set-up is
given by
2bh (qb-n-b) = RoC fan/ 8n (5)
This simple depth-averaged model can be improved using a complete perturba-
tion solution (similar to that used by Smith and McLean, 1983), but the
difficulty of obtaining high quality field data within a tidal inlet with
which to evaluate such theory caused us to use the simple theory outlined
above.
Field experiments covering five days (described in detail by Aubrey
and Speer, 1983) examined the magnitude of sea surface gradients, and
checked their consistency with channel bend theory. Maximum instantaneous
down-channel gradient over the five-day period during ebb tide was 0.0007
(thirty centimeters over the channel length separating the two sensors),
while maximum flood tide gradients were 0.0005 (twenty centimeters over
the same separation). Average maximum gradients over the five-day period
are the same for flood and ebb tide (18.5 cm over the instrument separa-
tion). From these gradients, a maximum shear stress of approximately 140
dynes/cm2 was calculated, where these shear stress estimates include not
only near-bed friction but also form drag, wave/current interaction, and
sediment transport effects (e.g., Grant and Madsen, 1982). Bed shear
stress is not easily separated from this total shear stress. Maximum cross-
channel set-up of approximately 5 cm was calculated from the down-channel
gradients, using equation (5), which represents a slope of 0.0009, similar
-44-
to the down-channel gradient. Field measurements show a cross-channel set-
up of complicated structure, with a magnitude of five-to-eight cm, most of
which is consistent with the simple model presented above. The remainder
of the observed set-up is of unknown hydrodynamic origin and not explained
by our simple theory.
Theory and observation are consistent with the analogy between Nauset
Inlet flow structure and river-bend flows, although neither the measure-
ments nor theory allow for in-depth comparison of the flow fields. Result-
ing inlet morphology is also consistent with the hypothesis that channel
bends are responsible for inlet migration. Nauset Inlet has both a steep
outer (northern) channel bank, and an accreting point bar on the inner
(southern) bank, similar to sedimentation patterns in river bends. Observ-
ation of Nauset Inlet since 1972 shows a migration pattern consistent with
the river bend analogy, with the south spit elongating and the north spit
shortening due to erosion. Although analogies between inlet bends and
river bends based on simple theory and observations of flow patterns and
sedimentation are incomplete, they indicate the potential importance of
curvature in inlet geometry on migration history of tidal inlets.
A conceptual model of inlet migration (figure 11) based on the three
mechanisms described above explains the unusual northward movement of
Nauset Inlet, opposite the longshore transport direction. When the inlet
is at its southernmost location, the estuary channels empty directly into
the ocean. There is no curvature to the flow (which could result in com-
plex flow non-uniformity), and the north barrier is not preferentially
eroded. Tidal flows are strong enough, however, to prevent material trans-
-45-
ported past the north spit from filling in the inlet channel. Bar bypass-
ing of littoral drift leads to accretion along the downdrift spit. If
storms do not halt this growth, the south spit can extend to the north and
eventually overlap the north spit, as occurred in the late 1960's and early
1970's. The base of the inlet channel retains its southerly location, and
the channel simply elongates to the north. In this configuration, the
north barrier remains essentially unchanged. This particular pattern has
been observed once in the last 30 years.
A different mechanism was responsible for the barrier overlap pattern
observed in the 1950's. In this instance, the northern barrier was
breached during a storm. The barrier remnant south of the breach attached
to Nauset Heights to form a relatively long southern spit. The base of
the inlet channel retained its southern location and extended through the
breach. Subsequently, the northern barrier lengthened by attachment to a
marshy island in the bay. The south spit further elongated through bar
bypassing, resulting in a pattern of overlapping spits. As in the 1965-
1972 pattern, the inlet channel lengthened as the south spit grew to the
north. The north spit remained relatively stable after attachment to the
bay island. Neither of these patterns is representative of the present
migration phase. The past ten years of movement have been characterized
by actual northward migration of the inlet channel and shortening of the
north spit, with no barrier overlap.
A storm breaching the north spit in 1972 caused this new migration
pattern to develop. The main inlet channel stabilized further north than
in previous storm breaches. As a result, the dominant ebb tidal flow was
constrained to flow to the north, and then east through the inlet channel,
setting up a channel bend flow pattern with erosion on the outer part of
-46-
the bend (north), and accretion on the inside of the bend (south). The
north wall of the inlet channel is presently eroding while a large sand
deposit is forming on the south bank of the channel. This "flow around a
bend" has existed for approximately ten years, leading to nearly 1 km of
northward inlet movement. This migration will probably continue until
either the inlet encounters an erosion-resistant substrate or a major storm
changes the inlet location. In the case of Nauset, the former is unlikely
(see Aubrey et al., 1982) since inlet tidal flows are currently eroding
peat deposits underneath the sandy barrier spits. Nothing more erosion-
resistant is likely to be encountered. Storm-induced inlet relocation is
a strong possibility. The long, frictionally dominated channels presently
carrying the tidal prism would probably be abandoned if a more southerly
breach were created by a storm. In that case, the large long-shore trans-
port could quickly close off the present inlet, which is nearly clogged by
the extensive ebb-tide delta. A more northerly breach created by storm
overwash is not likely to persist (as the February, 1978 blizzard demon-
strated) because the northern depths and tidal prism are too small. An
additional factor increasing the likelihood of breaching near Nauset Harbor
is the narrow width of the barrier at this point. This narrowing is caused
by erosion on the bay side of the barrier during ebb tide, as the easterly-
flowing tide is redirected northwards towards the present inlet (resulting
in another complex, channel-bend flow pattern).
The long-term fate of this estuary is affected by two dominant trends:
inlet migration (which contributes sediment to the estuary via flood tide
delta growth) and westward spit migration. Both of these factors reduce
the tidal prism, and consequently reduce the equilibrium cross-sectional
area of the inlet. The first factor has been discussed in detail. The
-47-
second factor, net onshore migration of the Nauset barrier beach, is appar-
ent in spite of large, higher frequency fluctuations (Speer et al., 1982).
The steady shoreward migration is a result of sea level rise combined with
overwash and inlet processes (barrier roll-over). Higher frequency oscil-
lations superimposed on this steady retreat result from inlet migration
episodes, seasonal beach changes, bar bypassing events, and large, near-
shore bedform generation (Aubrey, 1980). The effect of the onshore migra-
tion is a reduction in tidal prism (specifically by reduction of the area
of the back bay). Tidal prism is also reduced by deposition of sand as a
flood tide delta, an important factor since 1972, as the inlet has steadily
migrated northwards approximately 1 km. Vestiges of the former flood tidal
deltas are visible on recent aerial photographs of the area. As a result
of overwash and bay infilling, the stable inlet configuration will become
narrower and shallower with time (reduced equilibrium cross-sectional
area). This filling trend currently exceeds back-barrier deepening attri-
butable to sea-level rise, but anticipated increased rates of sea-level
rise (Aubrey and Emery, 1983) may reverse this trend.
SUMMARY
Three distinct patterns of natural inlet migration have been identified
from historical data (figure 11), and their underlying causes hypothesized.
These mechanisms explain the rare case where an inlet migrates in a direc-
tion opposite the dominant longshore sand transport, such as at Nauset
Inlet. Large variability in barrier spit length across a baymouth can also
be a reflection of these mechanisms. This rapid, spatially variable, inlet
migration contributes to infilling of some inlet/estuary complexes on a
geological time scale, as the continually enlarging flood tide delta
evolves at each inlet location. The result is an accelerated shrinkage of
-48-
some estuaries, with consequent reduction in inlet channel depth and width
(the decreased channel area responding to a reduced tidal prism). Whether
or not this flood tide delta growth significantly alters the fate of the
estuary depends on the hydraulic characteristics of the inlet and estuary
(flood tide delta growth is a function of flood/ebb flow dominance), as
well as long-term trends in sea-level rise.
The three distinct patterns of inlet migration are (figure 11):
1) Growth of the downdrift spit by addition of sediment from ebb tide
delta distal bars: some of these distal bars weld onto the downdrift spit
without escaping the inlet environment. The time scale of these growth
episodes is months, with an associated spit growth on a scale of 100 m.
Resultant spit change are relatively small compared to the other two growth
mechanisms. This mechanism can cause only updrift inlet migration.
2) Storm-induced shifts in inlet position associated with superele-
vated water levels: these changes are rare but significant, with time
scales of tens of years and spatial scales of hundreds of meters. Storm
breaches will remain stable and replace previous inlets if they are
hydraulically more efficient than alternative breaches. These major inlet
relocations have played an important role at Nauset Inlet, by shifting the
inlet position to the north (against the sense of net littoral drift) and
allowing the flow characteristics to set up a stable, steady northward
inlet migration independent of storm influences.
Storm effects in the future are expected to influence the Nauset barri-
ers significantly, and shift the inlet to the south. Since the southern-
most limit of the estuary/inlet system has historically been the preferred
position (because it is the most efficient location for tidal exchanges
-49-
between the ocean and bay), a breach at this narrow part of the barrier
will likely become the preferred inlet position. At present, a stable
dune-line is inhibiting storm overwash and breaching at this location.
3) Steady northward migration characterized by flow around a bend
(erosion on outside of bend, accretion on inside of bend) during ebb tides:
this migration has occurred since 1972 when a storm breach rapidly shifted
the inlet location, setting up a long, confined southern barrier-parallel
channel through which most tidal exchange takes place. Ebb flow through
this barrier-parallel channel must make a sharp bed through the inlet to
exit into the ocean. This bend creates a distinctive three-dimensional
flow pattern similar to river bend flows, eroding the north spit and
accreting to the south. The result is a steady northward migration which
will cease when a storm opens a breach further south of the present inlet;
this new breach will likely become the preferred inlet position. Flow cur-
vature resulting from complex inlet/tide channel geometry may be respons-
ible for both updrift and downdrift inlet migration at other locations,
playing an important role in barrier beach evolution.
-50-
REFERENCES
Aubrey, D.G., 1980. Our dynamic coastlines. Oceanus, v. 23, no. 4,
p. 4-13.
Aubrey, D.G. and P.E. Speer, 1983. Sediment transport in a tidal inlet.
Woods Hole Oceanographic Institution Techincal Report WHOI-83-20,
110 pp.
Aubrey, D.G. and P.E. Speer, in prep. A study of non-linear tidal propaga-
tion in shallow inlet/estuarine systems, Part I: Observations.
Aubrey, D.G., D.C. Twichell and S.L. Pfirman, 1982. Holocene sedimentation
in the shallow nearshore zone off Nauset Inlet, Cape Cod,
Massachusetts, Marine Geology, v. 47, p. 243-259.
Aubrey, D.G. and K.O. Emery, 1983. Eigenanalysis of recent United States
sea levels. Continental Shelf Research, v. 2, p. 21-33.
Bruun, P., 1978, Stability of Tidal Inlets. Elsevier, New York, 506 pp.
Bruun, P. and F. Gerritsen, 1960, Stability of Coastal Inlets. Amsterdam,
North Holland Pub. Co., 124 pp.
Dietrich, W.E., J.D. Smith and T. Dunne, 1979. Flow and sediment transport
in a river meander. Jour. Geology, v. 87, p. 305-315.
Emery, K.O., 1980. Relative sea levels from tide gage records. Proc. of
the National Academy of Sciences, v. 77, p. 6968-6972.
Fitzgerald, D.M., 1983. Sediment bypassing at mixed energy tidal inlets.
ASCE 18th Coastal Engineering Conference, Cape Town, South Africa.
Galvin, C., 1983. Shoaling with bypassing for channels at tidal inlets.
ASCE Coastal Engineering Conference, Cape Town, South Africa.
Grant, W.D. and O.S. Madsen, 1982. Moveable bed roughness in unsteady
oscillatory flow. Jour. Geophys. Res., v. 87, p. 469-481.
-51-
Hayden, B.P. and W. Smith, 1982. Season-to-season cyclone frequency pre-
diction. Monthly Weather Review, v. 110, p. 239-253.
Leatherman, S.P., 1979. Environmental geologic guide to Cape Cod National
Seashore. S.E.P.M. Field Guide Book, 249 pp.
Leatherman, S.P., A.J. Williams, and J.S. Fisher, 1977, Overwash sedimenta-
tion associated with a large scale northeaster. Marine Geology, v. 24,
p. 109-121.
Nouh, M.A. and R.D. Townsend, 1979. Shear-stress distribution in stable
channel bends. Jour. Hydr. Div., ASCE, v. 105, No. HY10, p. 1233-1245.
Nummedal, D., 1983. Barrier Islands. In Handbook of Coastal Processes and
Erosion, P.D. Komar (ed.), CRC Press, Boca Raton, FL, p. 77-121.
Redfield, A.C., and M. Rubin, 1962, The age of salt marsh peat and its
relation to recent changes in sea level at Barnstable, MA. Proc. Nat.
Acad. of Sciences, v. 48, p. 1728-1735.
Smith, J.D. and S.R. McLean, in prep. A model for meandering streams.
Speer, P.E., D.G. Aubrey and E. Ruder, 1982. Beach changes at Nauset
Inlet, Cape Cod, Massachusetts 1670-1981. Woods Hole Oceanographic
Institution Technical Report No. WHOI-82-40, 92 pp.
Speer, P.E. and D.G. Aubrey, in prep. A study of non-linear tidal propaga-
tion in shallow inlet/estuarine systems, Part II: Theory.
U.S. Army Corps of Engineers, 1969. Nauset Harbor, Orleans and Eastham,
Massachusetts, Survey Report, Department of the Army, New England
Division, Corps of Engineers, Waltham, Mass., 13 pp. + appendices.
U.S. Army Corps of Engineers, 1979, Cape Cod easterly shore beach erosion
study, v. 1, 11, 111. New England Division, Corps of Engineers,
Waltham, MA.
Zaremba, R., and S.P. Leatherman, 1979, Overwash processes and barrier
dynamics: Nauset Spit, Cape Cod, MA., U. MA-N.P.S.-C.R.U. Progress
Report, 245 p.
Zeigler, J.M., 1954. Beach Studies in the Cape Cod area conducted during
the period January 1, 1954 - June 30, 1954. Woods Hole Oceanographic
Institution, unpublished manuscript, reference number 54-59, 14 pp.
Zeigler, J.M., 1960, Cape Studies, Cape Cod, Aug. 1953 - April 1960. Woods
Hole Oceanographic Institution, unpublished report No. 60-20, 32 pp.
-53-
IN SHALLOW INLET/ESTUARINE SYSTEMS
The offshore tide becomes strongly distorted as it propagates into
shallow estuarine systems. Observations of sea surface elevation and hori-
zontal currents over periods ranging from three days to one year, at nine
stations within Nauset inlet/estuary, document the non-linear interaction
of the offshore equilibrium tidal constituents. Despite strong frictional
attenuation within the estuary, the overtides and compound tides of M2 ,
S2 and N2 , in particular, reach significant amplitude, resulting in strong
tidal distortion. High frequency forced constituents in sea surface are
phase-locked, consistently leading the forcing tides by 60*-70*, resulting
in a persistent distortion with falling tide longer than rising tide.
Forced constituents in currents are more nearly in phase with equilibrium
constituents, producing flood currents which are shorter but more intense
than ebb currents. A compound fortnightly tide, MSF, modulates the mean
water level such that lowest tides occur during Neap phase instead of
Spring phase. This fortnightly tide can be contaminated by storm surge,
changing the phase characteristics of this constituent. Implications of
the overtides, compound tides, and lower frequency tides on near-bed and
suspended material transport are profound.
-55-
The astronomical tide is strongly distorted during its propagation from
offshore into shallow inlet/estuarine systems common to the U.S. East and
Gulf Coasts. Time asymmetries develop in the rise and fall of the surface
tide with resulting time and amplitude asymmetries in the velocity field
(e.g., Boon and Byrne, 1981). This distortion can be represented as the
non-linear growth of harmonics of the principal ocean astronomical consti-
tuents (e.g., Dronkers, 1964; Pingree and Griffiths, 1979). Harmonic
growth is a result of finite amplitude effects entering through friction,
non-linear advection, and interactions with channel geometry as the tide
oscillates within the estuary. In the inlet/estuarine systems of interest
to this study, the water column is well mixed throughout most of the tidal
cycle and freshwater inflow forms a negligible part of the tidal prism.
The astronomical tide spectrum is composed of a large number of consti-
tuents whose mutual non-linear interactions represent a complex physical
problem (e.g., Munk and Cartwright, 1966; Gallagher and Munk, 1971).
Primary frequencies of interest are integral linear combinations of six
basic components related to celestial mechanics of the Earth-Moon-Sun
system:
f 1 day = period of Earth's rotation relative to the Sun =21 lunar month = period of Moon's orbital motion =31 year = period of Sun's orbital motion
8.85 years = period of lunar perigee fiS=18.61 years = period of regression of lunar nodes
20,900 years = period of solar perigee
Interactions between these basic frequencies result in other energetic
tidal frequencies, such as the inverse lunar day (fWj), where:
fl = fi - f2 + f3 = 0.966 fi
-56-
Tidal frequencies are divided into species which are separated by one
cycle/lunar day, into groups which are separated by one cycle/month, and
constituents which are separated by one cycle/year. Here we are concerned
with various predominant species and associated groups (table 1).
Compound constituents, which are linear combinations of basic frequen-
cies, can be generated through non-linear celestial and fluid mechanics.
For example, MSf consists of both a weak astronomical term and a potenti-
ally larger hydrodynamic term arising from M2 - Sz interactions, while
MS4 is a constituent arising solely from non-linear hydrodynamic interaction
of Mz and Sz. Similarly M4 , Mg, and M8 have no equilibrium tidal argument,
but reflect non-linear generation in oceanic basins of various scales.
Magnitude and phase of each observed constituent provides insight into
hydrodynamic processes.
The present study, along with its companion study (Speer and Aubrey,
1984), focuses on the distortion of the offshore tide as it propagates
through shallow estuarine systems connected to the ocean by a narrow tidal
inlet. Frictional decay of the offshore tide and harmonic growth of forced
constituents form the basis for examination of non-linear processes. Diag-
nostic numerical modeling examines the most important and representative
interactions observed in the field. Robinson, Warren, and Longbottom
(1983) reported a similar, but less comprehensive, study conducted in the
Fleet, on the south coast of England.
Along the US northeast coast, the principal tidal constituents of
interest are the M2 tide and its harmonics. The magnitude of Mz results
in it dominating non-linear processes during tidal propagation through the
estuary, although compound tides are also generated. In particular, M2 and
its first harmonic, M4, can be used to illustrate the dominant features of
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Constituent
Fortnightly
Diurnal
Semi-Diurnal
Ter-Diurnal
Quarter-Diurnal
Sixth-Diurnal
MS
01
K1
12.66 solar hours 12.42 solar hours 12.00 solar hours
8.18 solar hours
4.14 solar hours 4.00 solar hours
MK3
Species
-58-
tidal asymmetries in these systems (fig. 1). Two (arbitrary) phase relation-
ships between M 2 and M4 constituents (sea surface or velocity), can be
defined:
AM2 = ai cos (wt - 9) AN4 = az cos (2wt - O2)
For the case of sea surface, when M4 leads M2 by 90*, falling tide exceeds
rising tide in duration (fig. A). The phase relationship in this situa-
tion is:
261 - 6 2 = 90*
If we let the constituents refer to tidal velocity, with M2 and M4 in
phase, the case of shorter, enhanced flood currents is demonstrated. This
phase relationship can be expressed as:
201 = 0 2
The cases of symmetrical and enhanced ebb currents can be shown in a
similar manner.
The development of tidal asymmetries can have important effects on both
the geological evolution of shallow estuaries as well as on the short term
navigability of estuarine channels. An estuary characterized by shorter,
more intense flood then ebb currents (flood dominant) may be unable to
flush entering sediments effectively. Conversely, an estuary with stronger
ebb than flood currents (ebb dominant) may represent a more stable configu-
ration. The magnitude of the velocity asymmetry depends on the non-linear-
ity of the tide. Both flood- and ebb-dominated inlet/ estuarine systems
are found along the U.S. east coast (e.g., Nauset Inlet, flood dominant;
Wachapreague Inlet, ebb dominant). In addition to the different types of
asymmetry, these estuaries also exhibit varying degrees of non-linear
response to tidal forcing as measured by the ratio of amplitudes of M4 to
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TIDAL ASYMMETRIES FLOOD VERSUS EBB DOMINANCE
0 4 8 12 16 20 24 28 32 36 40 ELAPSED TIME (hours)
0 4 8 12 16 20 24 28 32 36 40 ELAPSED TiME (hours)
LEGEND FLOOD DOMINANT EBB DOMINANT Examples of tidal asymmetries for the case of M4/M 2=0.3. la) M4 is 90* out of phase with M2 . lb) M4 in phase and 1800 out of phase with M2'
0.
0
>0.
0,
ol
-60-
Mz (the M4 /M2 ratio). To better understand the problem of tidal propaga-
tion in a shallow inlet/estuarine complex, a field program and a numerical
modeling study were initiated at Nauset Inlet, Cape Cod, MA (fig. 2). This
paper details results of the field experiments examining the tidal response
of this estuary. Part II (Speer and Aubrey, 1984) focuses on diagnostic
models of the M2, M4 interactions.
The Nauset Inlet system is a salt marsh intersected by three major
tidal channels and connected to the ocean by a natural, unstabilized inlet
(fig. 3). The offshore tide is predominantly semi-diurnal with a range of
approximately two meters. The northern channel has extensive tidal flats
and mean depths less than one meter (fig. 3). Middle and south channels
have regions of tidal flats, channel depths of 2-3 m, and terminate in a
deeper body of water, Town Cove (4-6 m). The channels are well-mixed over
most of the tidal cycle and fresh water inflow is negligible. Nauset was
chosen for study because in terms of both channel geometries and tidal
asymmetry it is representative of many such systems on the US east coast.
II. FIELD METHODS
Two field experiments were undertaken at Nauset to examine the
characteristics of tidal propagation and to provide a data set against
which to test diagnostic numerical models of tide interactions. A two-
week experiment in September 1981 emphasized measurement of currents near
the inlet channel, some month-long measurements of tidal elevation through-
out the estuary, and measurement of sea surface gradients through the inlet
proper. The second field experiment, extending from August-October 1982,
included velocity and sea surface measurements to estimate local momentum
balances and a three month deployment of an array of tide gages. Experi-
mental instrumentation for 1982 (fig. 3) consisted of Steven's tide gauges
50 4 0
)NAL SEASHORE BEACH O R. L E A N S
MILE
NAUSET INLET LOW TIDE
21 SEPTEMBER 1981 -62-
AGA*
Location map for Nauset Inlet experiment of August through October, 1982. Numbered locations: 1-Goose Hummock (GH), 2-Mead's Pier (MP), 3-Snow Point (SP), 4-Middle Channel West (MCW), 5-Middle Channel East (MCE), 6-Nauset Heights (NH), 7-Ocean site, 8-Nauset Bay (NB), and 9-North Channel (NC). AGA refers to locations of four-day long deployments of an electromagnetic current meter array.
TOWN COVE,
Figure 3.
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(model nos. 71-A and 7030, made available by the NOAA National Ocean
Survey), a five-element array of electromagnetic current meters deployed
on a tripod (deployments typically lasting 2-4 days with sampling rates of
1 Hz), and numerous 2-7 day deployments of pressure sensors (Sea Data Model
TDR-la). The inlet was instrumented with four-day deployments of pressure
sensors in 1980 and 1981. These latter measurements yielded insight into
the interaction of tide and the narrow inlet channel, a region where long
term tide gauging is impractical. Further details of these experiments
may be found in Aubrey and Speer (1983).
Because of the sensitivity of estimates of harmonic tidal constituents
to errors in time base, attention was focused on annotating tide gage
records with precise time codes. Data from these tide gages were reduced
to a standard format either under contract to NOS at their facilities (with
either a one minute or six minute sample interval), or using a Calcomp
model 9000 coordinate digitizer to convert analog records to digital form
at the Woods Hole Oceanographic Institution. In both cases, proper quality
control on the time base was provided. Other data types were internally
recording on magnetic tape, with later processing at W.H.O.I.
III. STATISTICAL METHODS
Statistical analysis of the data sought to extract the amplitudes and
phases of major tidal constituents from both sea surface elevation (tide
gages and pressure sensors) and velocity (current meter) records. Experi-
mental logistics and instrument peculiarities produced data records of
varying duration at different areas of the estuary, making Fourier harmonic
analysis of limited use. Conventional fourier analysis requires 15- or
29-day record lengths to separate major harmonic components (M2 from S2
and M2 from N2 , respectively). Our records were either longer than this
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(in which case we wanted to utilize all the data and not just some subset)
or shorter than this, in which case we still wanted to extract tidal
components.
For records of 15-days or more duration, initial analysis utilized
standard power spectral techniques to determine the structure of the tide
at various points within the ocean/inlet/estuary system. Vector velocity
data was analysed via rotary component spectral analysis (Gonella, 1972)
to extract both frequency content as well as any tendency for rotary tidal
motion (negligible in long, straight channels, but potentially appreciable
near channel bends). Error analysis for this method is well-established,
with power spectral values following a chi-squared distribution, and phase
and coherence confidence limits described in Gonella (1972) following the
work by Goodman (1957).
square harmonic analysis, a variant of the standard Fourier harmonic
analysis technique developed by Schureman (1971). The goal of harmonic
analysis is to extract amplitudes and phases of the primary tidal harmonic
constituents and their compound tides. Finite record lengths and contami-
nation of tidal signals by noise introduced by storms and other sources,
com'bine to make harmonic analysis inexact, rendering estimation of confi-
dence intervals for these estimates of utmost importance. Methods for per-
forming harmonic analysis include: Fourier Harmonic Analysis (Schureman,
1971), the response or admittance method (Munk and Cartwright, 1966;
Cartwright, Munk and Zetler, 1969), and least-squares harmonic analysis
(Boon and Kiley, 1978). The techniques vary in their mathematical
approach, with consequent differences in error estimates. A thorough
-65-
review of the three techniques along with an intercomparison is provided
in Aubrey, Speer, and Boon (in prep.); a brief discussion of the techniques
is provided here.
Fourier Harmonic Analysis is performed on integral multiples of 15- or
29-day records of sea surface elevation or velocity. Record length is
determined by the need to resolve adjacent energetic tidal frequency bands.
Spectral estimates yield two degrees of freedom when the minimum record
length for maximum resolution is used. These estimates have confidence
limits given by a chi-square distribution, and suffer from the internal
aliasing due to finite record length (gate function in the time domain,
sinc function in the frequency domain), since the tidal constituents are
not integral multiples of elemental frequency bands. Low frequency and
unresolved tidal constituents must be inferred using formulae such as those
presented in Schureman (1971). Shorter record lengths are difficult to
quantitatively examine using Fourier Harmonic Analysis, because of the
resolution restrictions associated with this method. In particular, separ-
ation of the many constituents within semi-diurnal, quarter-diurnal, and
sixth-diurnal species from a short record is not possible. These restric-
tions led us away from the Fourier Harmonic Analysis in favor of other
schemes.
The response or admittance method was developed by Munk and Cartwright
(1966) as an alternative to the Fourier Harmonic Analysis method. The
method is based on spectrally relating a time series of long duration and
hence of excellent accuracy to an arbitrary length series at the same or
nearby location. The nomenclature arises from the admittance function, or
transfer function, relating two quantities in a spectral sense. The
Fourier transform of the admittance function is the impulse response func-
-66-
tion, which is convolved with the input series in the time domain to yield
an output function. Alternatively, the admittance (or transfer) function
is multiplied by the input transform to obtain the transform of the output
function. Ideally, the input function is derived from a suitably long
record of tidal data at a reference station, generated either from equili-
brium tidal theory, or lacking this, from a long time series of tides at
that coastal station. In the former case, the admittance function yields
a relationship between the measured tide over the period of interest and
the equilibrium tidal arguments. Infinite frequency resolution is poss-
ible if the admittance function is assumed to be smoothly varying on the
premise that (barring resonance) the response of the ocean to similar fre-
quencies is similar. For harmonic analysis purposes, the tide record
examined is related through this admittance procedure to a noise-free pre-
dicted tide for the same period. The part of the measured tide that is
coherent with the predicted tide is expressed in terms of a new admittance
function, whose statistical uncertainties have been derived in Munk and
Cartwright (1966). Relative amplitudes and phases for the admittance func-
tion derived from this analysis have simple confidence limits for the case
of small relative noise levels.
The admittance technique is useful for extracting that part of an
observed tide which is coherent with the reference station series, with
the remaining incoherent part of the signal interpreted as noise. To be
useful, the reference station and data station must have a similar response
to ocean tides. An admittance function' relating tides in the middle of the
ocean to tides within an embayment has limited value, and does not appreci-
ably improve a prediction generated by an alternate harmonic analysis
method. The extra work involved with the admittance procedure is not
-67-
justified in this situation. For the present study of non-linear tidal
harmonic generation in shallow estuaries, the admittance procedure was not
used for several reasons. First, there is no long time series of tides in
the estuarine system from which to extract response functions suitable for
generating noise-free reference series. Second, no local station is avail-
able from an environment physically similar to the estuarine system of
interest. A suitable reference station would require similar non-linear
response to discrete harmonic input; such a station is not available. This
points out the limited utility of the admittance technique in many shallow-
water coastal regions. The additional work required for a complete admit-
tance procedure represents another shortcoming compared to alternate tech-
niques. As a result, the procedure may not be justified except for certain
scientific studies where additional precision is made possible with an
appropriate long-term reference station.
The least squares harmonic analysis method provides several attractive
features which resulted in its adoption in this study. The least squares
method can be applied to any length time series, extracting tidal consti-
tuents without the resolution restrictions imposed by Fourier Harmonic
Analysis, and reducing internal aliasing by extracting the exact consti-
tuent frequency from the series, not the nearest integral multiple of the
fundamental frequency. The nearly infinite resolution of this technique,
termed super-resolution by Munk and Hasselman (1964), is attributable to
the least-square requirement that to determine phase and amplitude of a
signal of known frequency, only two data points are needed. For n frequen-
cies, then, only 2n data points are needed. No requirements are placed on
length of record or sample interval. The paradox between least-squares
analysis and Fourier harmonic analysis is resolved by proper analysis of
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noise levels in the data series. In particular, noise (defined as energy
due to non-tidal sources) at frequencies adjacent to tidal harmonic
frequencies limits the accuracies of harmonic least squares analysis, such
that a longer record will improve the estimates. Munk and Hasselman
(1964) first analysed the effect of noise on least-squares estimates of
two neighboring spectral lines. Filloux and Snyder (1979) extended the
algorithm for the noise analysis, deriving a form for estimating phase and
amplitude errors arising from least squares analysis.
Following Filloux and Snyder (1979), the sea surface elevation, C, at
tidal and lower frequencies is separated into harmonic, (H, and residual,
(R, components:
( = (H + CR
(H = 2 n(I In =1
n=l
where primes indicated estimated quantities, the n(1 represents the
complex amplitude corresponding to the n- h harmonic frequency, and In can
be defined as:
Iz1-1 = cos(Wnt + $n)
12n = sin(at + $n)
$. is the phase of the corresponding constituent of the equilibrium tide
evaluated at time zero. The phase of n( is relative to the equilibrium tide
at Greenwich, equivalent to G in Schuremann (1971). A scalar product is defined:
to+T
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where T is the record length. Conditions for solution of the least-squares
problem are set by differentiating (A2 with respect to the n(I 's:
2N 2 (InIm) m(i = (In,() n=1,2,...2N
m=l
m(= mnSi' (In,() n=l
where mnSr = (InIm), and Si1 is the inverse of St. These estimates can
be decomposed into three parts:
2N
,=2N+1 n=l
n=1
The first term is the true complex amplitude, the second represents errors
arising from tidal amplitudes not included in the analysis, and the third
term represents errors due to residual fluctuations. The second term can
be reduced by including a sufficient number of constituents in the analysis;
however these additional constituents adversely affect the third term. This
study includes twenty-nine terms in the analysis, with only four (MSF, M2 , M4 ,
Ms) of primary interest. Consequently, the second error term is small; the
third term is the larger error source. Using a definition of
ER (&) = 1 dT C (T)cos(rt
as the two-sided spectrum of CR, calculated from the covariance:
C (t) = <(R (x,t) (R(X,t+T)>
where angle brackets represent ensemble averaging, a co-variance matrix can be
calculated,
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(n~l M I>- <n I (MnI>
where the summation is over adjacent constituents within the same tidal
species. Using appropriate assumptions of quasi-stationarity in (R and
length of record T, Filloux and Snyder (1979) show:
iTER (Wn)2 npSiI mpSiI
where p,m,n refer to constituents of the same species. If
nDI = -arg .(H = -tan~ 1 (Zn-1I/2n(I)
|n(H| = mod n(H = (2n-1( 2 + 2n(I)2
and a covariance, V, is defined for brevity
V(a,B) = <aB3> - <a> <3>
are given as:
+ 2n(t 2 V(2 1(, 2(I)
In(A|4 V(n$0,n@A) =
V(In 14I, |n(i|)'2 and V(Hcn, Pi)'2'
Although algebraically complex, these expressions show the direct dependence
of errors on the noise spectrum, ER, while the Aca dependence shown by
Munk and Hasselman (1964) is implicit in the matrix Si .
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For this study, twenty-nine tidal constituents were extracted in a
least-squares sense, fourteen calculated directly with the remainder infer-
red using formulae provided in Schureman (1971). Of these, six species
were of particular interest (table 1), with all species except diurnal and
semi-diurnal containing considerable forced constituents. Once these
constituents were eliminated, the residual signal (regenerated from the
original series less the harmonic components) was analysed with a fast
Fourier transform, to generate estimates of the noise spectrum, ER. These
noise estimates were used to calculate errors in phase and amplitude
presented in tables 2, 3, and 4.
IV. RESULTS AND DISCUSSION
Harmonic analyses of 29-day records of sea surface elevation indicate
that Nauset is a strongly non-linear as well as frictionally dominated
inlet/estuarine system. The non-linear response to tidal forcing is
reflected in growth of high frequency M2 overtides, compound tides and a
forced low frequency MSf constituent throughout the estuary. The frictional
nature of the estuary is demonstrated both by large phase changes in the tide
(~76* in 2 km for the M2 constituent) and by amplitude decay of the total
spectrum (as much as 57 percent of the ocean range in 2 km).
Nine stations provide tidal data for examination of tidal distortion in
Nauset estuary (fig. 3)